Given $ m \angle BOC = 2x - 12$, and $ m \angle AOB = 9x + 16$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {9x + 16} + {2x - 12} = {180}$ Combine like terms: $ 11x + 4 = 180$ Subtract $4$ from both sides: $ 11x = 176$ Divide both sides by $11$ to find $x$ $ x = 16$ Substitute $16$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 2({16}) - 12$ Simplify: $ {m\angle BOC = 32 - 12}$ So ${m\angle BOC = 20}$.